is the indicator function.
Kernel \(T(X\mid x,u)\)  describes the probability of \(\textbf {{x}}\)  ending in set \(X\)  in one-step evolution given the current state \(x\)  and control \(u\) .
Given a control strategy \(\pi _\textbf {{x}}\)  and a time horizon \([0,N],\)  it is possible [1]} to define a probability measure \(P\)  over the paths of \(\textbf {{x}}_k\)  uniquely generated by \(T\)  and a (fixed) initial condition \(x_0\in \mathbb {R}^n\) 
such that
\(P[_{\textbf {{x}}}^N(0)\in X] = \mathbf {1}_{X}(x_0),\) 
